Solve for $x$ : $ 7|x - 1| + 9 = -4|x - 1| + 3 $
Solution: Add $ {4|x - 1|} $ to both sides: $ \begin{eqnarray} 7|x - 1| + 9 &=& -4|x - 1| + 3 \\ \\ { + 4|x - 1|} && { + 4|x - 1|} \\ \\ 11|x - 1| + 9 &=& 3 \end{eqnarray} $ Subtract ${9}$ from both sides: $ \begin{eqnarray} 11|x - 1| + 9 &=& 3 \\ \\ { - 9} &=& { - 9} \\ \\ 11|x - 1| &=& -6 \end{eqnarray} $ Divide both sides by ${11}$ $ \dfrac{11|x - 1|} {{11}} = \dfrac{-6} {{11}} $ Simplify: $ |x - 1| = -\dfrac{6}{11}$ The absolute value cannot be negative. Therefore, there is no solution.